Code for Geometry of Needle-Like Microstructures in Shape-Memory Alloyshttps://doi.org/10.60507/FK2/VZAIVFConti, SergioLenz, MartinRumpf, MartinVerhülsdonk, JanZwicknagl, Barbarabonndata2024-03-202024-03-22T08:13:56ZThis repository contains the code to <a href="https://doi.org/10.1007/s40830-023-00442-0">Conti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shap. Mem. Superelasticity (2023).</a> Needle-like microstructures are often observed in shape memory alloys near macro-interfaces that separate regions with different laminate orientation. We study their shape with a two-dimensional model based on nonlinear elasticity, that contains an explicit parametrization of the needle profiles. Energy minimization leads to specific predictions for the geometry of needle-like domains. Our simulations are based on shape optimization of the needle interfaces, using a polyconvex energy density with cubic symmetry for the elastic problem, and a numerical implementation via finite elements on a dynamically changing grid.Mathematical SciencesPhysicsConti, S., Lenz, M., Rumpf, M., Verhülsdonk, J., Zwicknagl, B., Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shap. Mem. Superelasticity (2023), doi, 10.1007/s40830-023-00442-0, https://doi.org/10.1007/s40830-023-00442-02024-03-20Lenz, Martin2024-03-20codeMIT